Game Semantics and Normalization by Evaluation

Pierre Clairambault (1, 2) , Peter Dybjer (3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages
3 CSE - Department of Computer Science and Engineering [Göteborg]

We show that Hyland and Ong's game semantics for PCF can be presented using normalization by evaluation (nbe). We use the bijective correspondence between innocent well-bracketed strategies and PCF Böhm trees, and show how operations on PCF Böhm trees, such as composition, can be computed lazily and simply by nbe. The usual equations characteristic of games follow from the nbe construction without reference to low-level game-theoretic machinery. As an illustration, we give a Haskell program computing the application of innocent strategies.

Mots clés: game semantics; normalization by evaluation

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Pierre Clairambault, Peter Dybjer. Game Semantics and Normalization by Evaluation. 18th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), Apr 2015, Londres, United Kingdom. ⟨10.1007/978-3-662-46678-0_4⟩. ⟨hal-01286469⟩